Can I influence the bone envelopes?
You can't modify the bone envelope's scale at individual axis, separately. 

A bone's envelope distance is stored as a single attribute envelope_distance, without any way to modify it for a single axis. This is unlike b-bone scale which is stored separately in bbone_x and bbone_z, thus can be scaled separately. 

Your only choice here is through weight painting, already elaborated in the other answers posted before mine.